observe and prove the constant length of the great year.[1] Next, in determining the motions of both these and the five other planets, they did not use the same principles and assumptions or even the same demonstrations of the appearances of revolutions and motions. For some used only homocentric circles; others, eccentrics and epicycles, which on being questioned about, they themselves did not fully comprehend. For those who put their trust in homocentrics, although they proved that other diverse motions could be derived from these, nevertheless they could by no means decide on any thing certain which in the least corresponded to the phenomena. But these who devised eccentrics, even though they seem for the most part to have represented apparent motions by a number [of eccentrics] suitable to them, yet in the meantime they have admitted quite a few which appear to contravene the first principles of equality of motion. Another notable thing, that there is a definite symmetry between the form of the universe and its parts, they could not devise or construct from these; but it is with them as if a man should take from different places, hands, feet, a head and other members, in the best way possible indeed, but in no way comparable to a single body, and in no respect corresponding to each other, so that a monster rather than a man would be constructed from them. Thus in the process of proof, which they call a system, they are found to have passed over some essential, or to have admitted some thing both strange and scarcely relevant. This would have been least likely to have happened to them if they had followed definite principles. For if the hypotheses they assumed were not fallacious, everything which followed out of them would have been verified beyond a doubt. However obscure may be what I now say, nevertheless in its own place it will be made more clear.
"When therefore I had long considered this uncertainty of traditional mathematics, it began to weary me that no more definite explanation of the movement of the world machine established in our behalf by the best and most systematic builder of all, existed among the philosophers who had studied so exactly in other respects the minutest details in regard to the sphere. Wherefore I took upon myself the task of re-reading the books of all the philosophers which I could obtain, to seek out whether any one had ever conjectured that the motions of the spheres of the universe were other than they supposed who taught mathematics in the schools. And I found first that, according to Cicero, Nicetas had thought the earth was moved. Then later I discovered according to Plutarch that certain others had held- ↑ i. e., the 15,000 solar years in which all the heavenly bodies complete their circuits and return to their original positions.
